paper-polyhedra

Paper Models of Polyhedra
Gijs Korthals Altes
Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers,
mathematicians and artists for millennia

Copyrights © 1998-2001 Gijs.Korthals Altes All rights reserved .
It's permitted to make copies for non-commercial purposes only
email: gijs@korthals.altes.net

Paper Models of Polyhedra
Platonic Solids
Dodecahedron
Cube and Tetrahedron
Octahedron
Icosahedron
Archimedean Solids
Cuboctahedron
Icosidodecahedron
Truncated Tetrahedron
Truncated Octahedron
Truncated Cube
Truncated Icosahedron (soccer ball)
Truncated dodecahedron
Rhombicuboctahedron
Truncated Cuboctahedron
Rhombicosidodecahedron
Truncated Icosidodecahedron
Snub Cube
Snub Dodecahedron
Kepler-Poinsot Polyhedra
Great Stellated Dodecahedron
Small Stellated Dodecahedron
Great Icosahedron
Great Dodecahedron
Other Uniform Polyhedra
Tetrahemihexahedron
Octahemioctahedron
Cubohemioctahedron
Small Rhombihexahedron
Small Rhombidodecahedron
S mall Dodecahemiododecahedron
Small Ditrigonal Icosidodecahedron
Great Dodecahedron
Compounds
Stella Octangula
Compound of Cube and Octahedron
Compound of Dodecahedron and Icosahedron
Compound of Two Cubes
Compound of Three Cubes
Compound of Five Cubes
Compound of Five Octahedra
Compound of Five Tetrahedra
Compound of Truncated Icosahedron and Pentakisdodecahedron

Other Polyhedra
Pentagonal Hexecontahedron
Pentagonalconsitetrahedron
Pyramid
Pentagonal Pyramid
Decahedron
Rhombic Dodecahedron
Great Rhombihexacron
Pentagonal Dipyramid
Pentakisdodecahedron
Small Triakisoctahedron
Small Triambic Icosahedron
Polyhedra Made of Isosceles Triangles
Third Stellation of the Icosahedron
Sixth Stellation of the Icosahedron
Seventh Stellation of the Icosahedron
Eighth Stellation of the Icosahedron
Ninth Stellation of the Icosahedron
Final Stellation of the Icosahedron
Prism and Antiprism
Triangular Prism
Pentagonal Prism
Pe ntagonal Antiprism
Triangular Prism
Octagonal Prism
Octagonal Antiprism
Pentagrammic Prism
Pentagrammic Antiprism
Hexagrammic Prism
Hexagrammic Antiprism
Twisted Rectangular Prism
Kaleidocycles
Hexagonal Kaleidocycle
Octagonal Kaleidocycle
Decagonal Kaleidocycle
Other Paper Models
Cylinder
Tapered Cylinder
Cone
Special Cones
"Matryoska house"
"Matryoska house" 50%
Globe
Chevaux-de-frise

1
Dodecahedron
3
7
5
11
9.
2
12
4
10
6.
8

Dodecahedron

Dodecahedron

Cube
Tetrahedron

4
Cube
5 1 2 6
3
4
3
Tetrahedron
2
1

Octahedron

Icosahedron

Cuboctahedron

Icosidodecahedron

Truncated Tetrahedron

Truncated Octahedron

Truncated Cube

Truncated icosahedron

Truncated dodecahedron

Rhombicuboctahedron

Truncated cuboctahedron

Rombicosidodecahedron

Truncated Icosidodecahedron

Snub cube

Snub cube
Right-handed

Snub dodecahedron

Snub dodecahedron
Right-handed

Small Stellated Dodecahedron
On this page a model out
of one piece On the next pages
a model out of six pieces.
Fold the long lines backwards
fold the short lines forwards

1
2

3
4

5
6

Octahemioctahedron
8
type 1
type 2
7
13
11
5
12
6
2
10
1
3 4
14
13

Cubohemioctahedron

Small Rhombidodecahedron
(small version)
Fold the dotted lines forwards
Fold the other lines

Small Rhombidodecahedron
(large version)
Fold the dotted lines forwards
Fold the other lines
A
B
F
C
E
D

B
A

C
A

D
A

E
A

F
A

Small dodecahemiododecahedron
Folds the lines between the
triangles forwards. Folds the
other lines backwards.

Great Stellated Dodecahedron
made out of one piece of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.

Great Stellated Dodecahedron
made out of two pieces of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.
This is piece one. On the next page
is piece two.
1

Great Stellated Dodecahedron
made out of five pieces of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.
N= Next part P= Previous part
N
P

Great Stellated Dodecahedron
made out of five pieces of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.
N= Next part P= Previous part
N
P

Great Stellated Dodecahedron
made out of five pieces of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.
N= Next part P= Previous part
N
P

Great Stellated Dodecahedron
made out of five pieces of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.
N= Next part P= Previous part
N
P

Great Stellated Dodecahedron
made out of five pieces of paper.
Cut the lines between the long
and the short sides of the triangles.
Fold the long lines backwards and
fold the short lines forwards.
N= Next part P= Previous part
N
P

Pentagonale hexacontahedron

2
1

4
3

6
5

8
7

10
9

Pentagonallconssitetrahedron

Stella Octangula
Type 1
Type 2
Fold lines of type 1
backwards
Fold lines of type 2
forwards

Fold the lines
with a rightangle
backwards
fold the other
lines forwards
Compound of two
Cubes

Compound of Three Cubes
(Small version)
Fold the dotted liines forwards
Fold the other lines backwards

Compound of Three Cubes
(Small version)
Fold the dotted liines forwards
Fold the other lines backwards
D
A
C
C
E
E
B
F
G
G

B
A
C
A
A

D
A
E
A
A

F
A
A
A
G

On this page a compound of five cubes
made of one piece of paper.
On the next pages a compound of five
cubes made of 7 pieces of paper

Instructions:
Cut and fold the piece(s) of paper.
Glue the part without tabs around it last.
This is the top part of piece F. This one
opposites the center part of piece A.
Below an example of a part
Fold forwards
Fold backwards

B
B
A
G
C
G
C
D
D
F
F
E
E

B
A
A

C
A
A
D
A
A

E
A
A
F
A
A

G
A
A

Compound of five Octahedra
If you use paper in five different colors
each octahedron has a different color
Color 1
A
D
H
G
E
R
C
I
B
U
M
d
P
F
N
O
Y
Q
L
c
W
K
a
T
J
S
X
Z
V
b

Compound of five Octahedra
Color 2
B
F
K
J
G
W
A
D
C
L
N
O
Q
S
E
R
d
c
M
P
U
T
Z
Y
V
X
H
b
I
a

Compound of five Octahedra
Color 3
C
I
L
D
J
K
B
M
A
Y
O
P
R
Q
F
S
N
G
E
H
V
W
X
b
a
Z
T
d
U
c

Compound of five Octahedra
Color 4
D
K
F
O
L
P
A
B
E
G
I
H
S
R
U
Q
C
T
J
a
X
Z
d
b
Y
c
V
M
W
N

Compound of five Octahedra
Color 5
E
N
G
R
O
H
D
F
A
B
J
C
T
V
I
U
K
a
W
S
Y
X
c
d
Z
b
L
P
M
Q

Pyramids

Pentagonal pyramid

Decahedron

Rhombic Dodecahedron

Great Rhombihexacron
X
X
X
X
Fold the short lines forwards
Fold the long lines backwards

Pentagonal Dipyramid

Pentakisdodecahedron
X
X
X
X

‘Dodecahedron’
A convex dodecahedron
(not a platonic solid)
constructed of 12
isosceles triangles

Hexakaidecahedron

‘Icosahedron’
A convex icosahedron
(not a platonic solid)
constructed of 20
isosceles triangles

Icositetrahedron

Icosioctahedron

Tricontidihedron

Tricontihexahedron

Tetracontahedron

Hecatohedron

Third Stallation of the Icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
X
X
X
X

Third Stallation of the Icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
X
X
X
X

Sixth Stallation of the Icosahedron
(small version)
Fold the dotted lines forwards
Fold the other lines backwards
First glue part A
Glue the parts A-M on A
Part A:
X
X
X
X

Parts B-M

Sixth Stallation of the Icosahedron
(large version)
First glue the parts A until F
Glue the 12 other parts on the ABCDEF
C
D
B
E
A
F

Sixth Stallation of the Icosahedron
(large version)
B
A

Sixth Stallation of the Icosahedron
(large version)
C
A

Sixth Stallation of the Icosahedron
(large version)
D
A

Sixth Stallation of the Icosahedron
(large version)
E
A

Sixth Stallation of the Icosahedron
(large version)
A
F

Sixth Stallation of the Icosahedron
(large)

Sixth Stallation of the Icosahedron
(large)

Sixth Stallation of the Icosahedron
(large)

Sixth Stallation of the Icosahedron
(large)

Sixth Stallation of the Icosahedron
(large)

Sixth Stallation of the Icosahedron
(large)

Seventh Stellation of the Icosahedron
A
D
B
B
D
C
C
B
G
A
A
G
F
F
C
I
A
A
I
H
H

Seventh Stellation of the Icosahedron
D
E
A
A
E
J
J
E
F
D
D
F
L
L
F
B
E
E
B
N
N

Seventh Stellation of the Icosahedron
G
H
B
B
H
O
O
H
C
G
G
C
Q
Q
I
J
C
C
J
R
R

Seventh Stellation of the Icosahedron
J
D
I
I
D
K
K
K
L
J
J
L
S
S
L
E
K
K
E
M
M

Seventh Stellation of the Icosahedron
M
N
L
L
N
T
T
N
M
O
O
M
F
F
O
G
N
N
G
P
P

Seventh Stellation of the Icosahedron
P
Q
O
O
Q
T
T
Q
H
P
P
H
R
R
R
I
Q
Q
I
S
S

Seventh Stellation of the Icosahedron
S
K
R
R
K
T
T
T
P
M
M
P
S
S

Eighth Stellation of the Icosahedron
(Large version)
Lold dotted lines forwards
Fold other lines backwards
B
B
C
C
D
A
D
E
E
F
F

Eighth Stellation of the Icosahedron
(Large version)
Lold dotted lines forwards
Fold other lines backwards
B
A
A

Eighth Stellation of the Icosahedron
(Large version)
Lold dotted lines forwards
Fold other lines backwards
C
A
A

Eighth Stellation of the Icosahedron
(Large version)
Lold dotted lines forwards
Fold other lines backwards
D
A
A

Eighth Stellation of the Icosahedron
(Large version)
Lold dotted lines forwards
Fold other lines backwards
E
A
A

Eighth Stellation of the Icosahedron
(Large version)
Lold dotted lines forwards
Fold other lines backwards
A
A
F

Ninth Stellation of the Icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
C
F
B
A
B
A
A
F
F
B
C
C
E
G
E
G
D
D
C
K
K
F
B
C
A
A
A
A
C
D
D
E
D
E
H
I
H
I
G
G
B
H
H
C
D
E
A
A
E
A
F
A
F
B
F
B
J
K
J
K
I
I
D
J
J
E

K
I
G
L
J
H
B
B
C
C
H
H
L
L
K
K
G
G
C
C
D
D
I
I
L
L
D
D
E
E
J
J
L
H
H
K
K
L
L
I
I
E
E
F
F
B
B
F
F
J
J
L
L
G
G
G
G
H
H
I
I
J
J
K
K
L

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
A
B
C
F
D
E

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
B
A
F
C
K
G

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
C
A
B
D
G
H

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
D
A
C
E
H
I

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
E
A
D
F
I
J

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
F
A
E
B
J
K

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
G
B
K
C
L
H

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
H
C
G
D
L
I

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
I
D
H
E
L
J

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
J
E
I
F
L
K

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
K
F
J
B
L
G

Final Stellation of the icosahedron
Fold the dotted lines forwards
Fold the other lines backwards
L
G
K
H
J
I

Triangular prisms

Pentagonal Prism

Pentagonal Antiprism

Octagonal Prism

Octagonal Antiprism

Pentagrammic Prism
Fold the dotted lines forwards
Fold the other lines backwards

Pentagrammic Antiprism
Fold the dotted lines forwards
Fold the other lines backwards

Hexagrammic Prism
Fold the dotted lines forwards
Fold the other lines backwards

Hexagramic Antiprism
Fold the dotted lines forwards
Fold the other lines backwards

Twisted rectangular prism (45 degrees)

Twisted rectangular prism (90 degrees)

Twisted rectangular prism (+ 45 -45 degrees)

Kaleidocyclus

Caleidocyclus 8

Caleidocyclus 10

Cylinder

Tapered Cylinder
l
n
x
l =
r
2
+ h
2
c = 2
r1
x = 360.2.
. l / c
d = c . n / l
r1
r2
r1 = radius
r2 = radius
c = circumference of circle 1
d = circumference of circle 2
x =angel of the part of the large circle
l = radius of the large circle
h = height of the cone
i = heigt of the tapered cylinder
= pi = 3.1415

Cone
l
x
l =
r
2
+ h
2
c = 2
r
x = 360.2.
. l / c
r
r = radius
c = circumference of the circle
x =angel of the part of the large circle
l = radius of the large circle
h = height of the cone
= pi = 3.1415

Asymetric Cone

Square Cone

Square Cone

Paper Colour 1/ papier kleur1
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor

Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house

paper colour 2 / papier kleur 2
(uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place
dormerwindow

onderkant dak/
bottom roof
fits around walls
don't glue roof on the
walls
Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2

Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
Paper Colour 1/ papier kleur1
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor
Paper Colour 1/ papier kleur1
Paper Colour 1/ papier kleur1
dakkapel
dormer-window
zuidelijke en westelijke muur huis
south and west wall house
noordelijke, oostelijke muur huis en de bodem
north, east wall of the house and the floor

onderkantdak plus twee zijden
two sides of the roof
onderkantdak plus twee zijden
two sides of the roof
place
dormerwindow
window
place
dormerwindow
paper colour 2 / papier kleur 2
(uitsnijden / cut-out)
paper colour 2 / papier kleur 2
(uitsnijden / cut-out)
Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof
fits around walls
don't glue roof on the
walls
Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof
fits around walls
don't glue roof on the
walls
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof
fits around walls
don't glue roof on the
walls
(uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2
paper colour 2 / papier kleur 2
onderkant dak/
bottom roof
fits around walls
don't glue roof on the
walls
(uitsnijden / cut-out)
onderkantdak plus twee zijden
two sides of the roof
place
place
dormerwindow
dormer-
Twee zijden dak
Two sides of the roof
paper colour 2 / papier kleur 2

Globe

1
3
2
1
2
3
1
3
2
1
2
3
1
3
2
1
2
3
1
3
2
1
2
3
1
3
2
1
2
3
1
3
2
1
2
3
1
3
2
1
2
3
1
3
2
1
2
3

Large Chevaux-de-frise
The other two parts are on the next two pages
3
1 1

1
2 2

3
2 2